# Editing Prefix sum array and difference array

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==Use of difference array== | ==Use of difference array== | ||

− | The difference array is used to keep track of an array when ranges of said array can be updated all at once. If we have array <math>A</math> and add an increment <math>k</math> to elements <math>A_i, A_{i+1}, ..., A_{ | + | The difference array is used to keep track of an array when ranges of said array can be updated all at once. If we have array <math>A</math> and add an increment <math>k</math> to elements <math>A_i, A_{i+1}, ..., A_{j-1}</math>, then notice that <math>D_0, D_1, ..., D_{i-2}</math> are not affected; that <math>D_{i-1} = A_i - A_{i-1}</math> is increased by <math>k</math>; that <math>D_i, D_{i+1}, ..., D_{j-2}</math> are not affected; that <math>D_{j-1} = A_j - A_{j-1}</math> is decreased by <math>k</math>; and that <math>D_j, D_{j+1}, ...</math> are unaffected. Thus, if we are required to update many ranges of an array in this manner, we should keep track of <math>D</math> rather than <math>A</math> itself, and then integrate at the end to reconstruct <math>A</math>. |

===Example: Wireless (CCC)=== | ===Example: Wireless (CCC)=== |